The above posts have already told you some of the best fps based good storyline games. Now, I will tell you some other good games that come with good storylines.
NFS The Run: I'm sure you are already aware of Need for Speed series and know how good their games are. 'NFS The Run' features a grand race which you have to win in order to earn a big amount and pay off your debts. While playing the storyline, you will encounter in between stories which will insist you to continue playing this game further.
Spec Ops The Line: This is also a good fps game which my fellow members forget to tell. In terms of storyline, this game has been rated for the best sad storyline. The gameplay features some exciting actions like shooting sand filled cars that make the enemy drown in the intense layers of sand. The graphics also feature some exciting textures and lightning features.
GTA 4: Well, if you want to play a good storyline game then you just cannot forget to play this game. The game features excellent graphics and actions. The game is so much addictive that you will not leave your PC without completing the missions and getting a short glimpse of the storyline.
L.A. Noire: This is yet another incredible game from 'RockStar'. This is the first RockStar game that does not revolve around the gangster theme. In this game you will play the role of a detective who solves the mystery of gruesome murders. To be a perfect player in this game, you will need to perfect your skills of studying the facial expressions.
I hope this was useful for you.